I. Technical Field
This invention pertains to wireless telecommunications, and particularly to detection of information transmitted over a radio interface.
II. Related Art and Other Considerations
In a typical cellular radio system, a wireless terminal communicates via a radio access network (RAN) to one or more core networks. The wireless terminal can be a mobile station (also termed “user equipment unit” (“UE”) or “mobile terminal”) such as a mobile telephone (“cellular” telephone) and laptop with mobile termination, and thus can be, for example, a portable, pocket, hand-held, computer-included, or car-mounted mobile device which communicates voice and/or data with the radio access network. Alternatively, the wireless terminal can be a fixed wireless device, e.g., fixed cellular devices/terminal which is part of a wireless local loop or the like.
The radio access network (RAN) covers a geographical area which is divided into cell areas, with each cell area being served by a base station. A cell is a geographical area where radio coverage is provided by the radio base station equipment at a base station site. Each cell is identified by a unique identity, which is broadcast in the cell. The base stations communicate over the air interface (e.g., radio frequencies) with the wireless terminal within range of the base stations. In the radio access network, several base stations are typically connected (e.g., by landlines or microwave) to a radio network controller (RNC). The radio network controller, also sometimes termed a base station controller (BSC), supervises and coordinates various activities of the plural base stations connected thereto. The radio network controllers are typically connected to one or more core networks.
Thus, wireless communications involve transmission of information over an air or radio interface from a transmitter station to a receiver station. For example, a mobile transmitter station (e.g., mobile station) may send a message on an uplink channel to a receiver unit such as a base station. Conversely, a transmitter unit in the form of a base station may send a message on a downlink channel to a receiver of a mobile station, or even to receivers in plural mobile stations.
In some instances a transmission between stations includes a particular sequence of samples. The sequence can be used to identify a particular transmitting station and/or to facilitate synchronization between the transmitting unit of one station and the receiving unit of another station. When associated for such purposes with a particular station, the sequence is known as a “signature sequence”. For example, a base station may have a particular signature sequence included in certain transmissions to distinguish that particular base station from other base stations whose signals may be also be received by mobile stations. Similarly, a mobile station may be assigned a certain signature sequence, at least temporarily (e.g., per connection, while in a specified cell), so that when the signature sequence is included in a wireless transmission on the uplink to a base station node, the base station node can determine that the transmissions emanated from that mobile station rather than other mobile stations in the cell of the base station node.
The design of signature sequences with small auto and cross correlation has been studied in a wide range of applications including wireless communication and radar. Of particular interest in wireless communication is the need to design a large number of unique sequences for the purpose of synchronization and device identification, as briefly mentioned above. Examples include the Barker sequence, chirp-like sequences, the m-sequence, and the Gold sequence derived from it. In radar signal design, there is also a wealth of literature on sequences with good properties for the detection of targets with different delay-Doppler shifts.
The general principle of introducing delay-Doppler shift to a base sequence for identification purpose has been disclosed in U.S. patent application Ser. No. 11/292,415, filed Dec. 2, 2005, entitled “HOPPING PILOT PATTERN FOR TELECOMMUNICATIONS, which is incorporated by reference herein in its entirety.
The ability of a pair of signature sequences to be distinguished from each other is often measured by their cross correlation function defined by Expression (1), in which N is the sequence length.
                                          ∑                          n              =              0                                      N              -              1                                ⁢                                          ⁢                                                    s                o                            ⁡                              [                n                ]                                      ⁢                                          s                1                *                            ⁡                              [                n                ]                                                    ,                            (        1        )            In a time-dispersive (frequency selective) channel, a good signature sequence also needs to be able to distinguish itself from its multipath echos. This is measured by its auto correlation function defined by Expression (2) for τ=0, . . . N−1.
                                          ∑                          n              =              0                                      N              -              1                                ⁢                                          ⁢                                                    s                o                            ⁡                              [                n                ]                                      ⁢                                          s                0                *                            ⁡                              [                                  n                  -                  τ                                ]                                                    ,                            (        2        )            Unless otherwise specified, all the indexing or offsetting utilized herein is modulo N. This results in the circular operations that can be achieved in practice by introducing cyclic prefix of appropriate length commonly seen in an OFDM system.
Therefore, the most commonly used metric for sequence design in a time-dispersive channel is simply the cross correlation function defined as by Expression (3).
                                          ϕ                                          s                o                            ,                              s                1                                              ⁡                      [            τ            ]                          ≡                              ∑                          n              =              0                                      N              -              1                                ⁢                                          ⁢                                                    s                o                            ⁡                              [                n                ]                                      ⁢                                                            s                  1                  *                                ⁡                                  [                                      n                    -                    τ                                    ]                                            .                                                          (        3        )            In the case where s0[n]=s1[n], the cross-correlation function becomes an auto correlation function. A good sequence set should then have small cross correlation between any pair of sequences at all lags and small auto correlation at non-zero lag for all individual sequences. In cases where the system is synchronized up to the sequence length, the same sequence can be circularly shifted and assigned to more than one device as long as the relative circular shifts are more than the channel's maximum delay spread. The common pilot code for CDMA2000 is such an example.
One example of sequence set with good auto and cross correlation function is the Zadoff-Chu sequence described in B. M. Popovic, “Spreading Sequences for Multi-Carrier CDMA Systems,” IEEE Colloquium on CDMA Technologies and Applications for Third Generation Mobile Systems, May 19, 1997, incorporated by reference herein, and defined by Expression (4).
                                                        s              u                        ⁡                          [              n              ]                                =                      exp            ⁢                          {                                                -                  j2                                ⁢                                                                  ⁢                π                ⁢                                                                  ⁢                u                ⁢                                                      n                    ⁡                                          (                                              n                        +                        1                                            )                                                                            2                    ⁢                    N                                                              }                                      ,                            (        4        )            In Expression (4), n=0,1, . . . , N−1 and the sequence index u also ranges from 0 to N−1. The auto correlation function of any individual Zadoff-Chu sequence is zero except for the zero lag where it is N and the cross correlation between any pair of distinctive Zadoff-Chu sequences is √{square root over (N)} for all lags. For identification, a device may be assigned a unique sequence index u and a circular shift k, as proposed to the Long Term Evolution in 3GPP, “E-UTRA Random Access Preamble Design”, TSG-RAN WG1 #44bis, R1-060998, Athens, Greece, Mar. 27-31, 2006, incorporated herein by reference.
Another example is the set of N+2 Gold sequences derived from a pair of preferred m-sequences with a maximum cross-correlation of √{square root over (2N)} and described in J. G. Proakis, “Digital Communications 2nd Edition,” McGraw Hill, 1989, pp. 834-835, incorporated herein by reference.
The good correlation properties of the existing designs described above are valid only when there is no frequency uncertainty in the communication environment. In reality, the channel may be time-selective (or frequency dispersive) due to Doppler spread. There may also be frequency offset among the communication devices due to unsynchronized oscillators. These frequency uncertainties, together with the channel's time dispersion, are best described by the (noiseless) received signal at the channel output given by expression (5).
                              r          ⁡                      [            n            ]                          =                              ∑                          τ              =              0                                                      τ                max                            -              1                                ⁢                                          ⁢                                    ∑                              v                =                0                                                              v                  max                                -                1                                      ⁢                                                  ⁢                                          h                ⁡                                  [                                      τ                    ,                    v                                    ]                                            ⁢                              s                ⁡                                  [                                      n                    -                    τ                                    ]                                            ⁢                              ⅇ                                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                    π                    ⁢                                                                                  ⁢                    vn                                    N                                                                                        (        5        )            
In Expression (5), h(τ,ν) is the channel's delay-Doppler response with maximum delay-Doppler spread (τmax, νmax). Note that the frequency offset is incorporated into the Doppler spread of the channel.
To detect the sequence, the receiver then needs to match the received signal with a hypothesis of the unknown delay-Doppler spread. This is accomplished by the two-dimensional delay-Doppler correlator given by Expression (6).
                                                                        I                ⁡                                  [                                      τ                    ,                    v                                    ]                                            =                                                ∑                                      n                    =                    0                                                        N                    -                    1                                                  ⁢                                                                  ⁢                                                      r                    ⁡                                          [                      n                      ]                                                        ⁢                                                            s                      *                                        ⁡                                          [                                              n                        -                        τ                                            ]                                                        ⁢                                      ⅇ                                          -                                                                        j                          ⁢                                                                                                          ⁢                          2                          ⁢                                                                                                          ⁢                          π                          ⁢                                                                                                          ⁢                          vn                                                N                                                                                                                                                                                    =                                                      ∑                                                                  τ                        1                                            =                      0                                                              N                      -                      1                                                        ⁢                                                                          ⁢                                                            ∑                                              v                        =                        0                                                                    N                        -                        1                                                              ⁢                                                                                  ⁢                                                                  ⅇ                                                                              j2π                            ⁡                                                          (                                                              v                                -                                                                  v                                  ′                                                                                            )                                                                                ⁢                                                      τ                            ′                                                                                              ⁢                                              h                        ⁡                                                  [                                                                                    τ                              ′                                                        ,                                                          v                              ′                                                                                ]                                                                    ⁢                                                                        X                          s                                                ⁡                                                  [                                                                                    τ                              -                                                              τ                                ′                                                                                      ,                                                          v                              -                                                              v                                ′                                                                                                              ]                                                                                                                                ,                                                          (        6        )                                                      X            s                    ⁡                      [                          τ              ,              v                        ]                          =                              ∑                          n              =              0                                      N              =              1                                ⁢                                          ⁢                                    s              ⁡                              [                n                ]                                      ⁢                                          s                *                            ⁡                              [                                  n                  -                  τ                                ]                                      ⁢                          ⅇ                                                -                  j                                ⁢                                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                    vn                                    N                                                                                        (        7        )            In Expression (6), Expression (7) is the (circular) ambiguity function.
Therefore, the measure of a sequence's ability to be uniquely identified in a time-frequency selective channel should be the two-dimensional ambiguity function given by Expression (7). An ideal sequence should have an ambiguity function resembling a thumbtack with sharp peak at the origin and an evenly distributed low sidelobe. The one-dimension auto and cross correlation functions conventionally used for measuring signature sequence properties fail to reveal the sequence's characteristics in the presence of frequency uncertainty.
FIG. 16 shows an ambiguity function of a length N=29 Zadoff-Chu sequence with u=6. It is clear that for ν=0 (no frequency uncertainty), the correlation property is ideal. However, there are two peaks at (τ=24, ν=1) and (τ=5, ν=28). This implies that the sequence is identical to itself shifted in time and frequency by the corresponding amounts. Therefore, if there is a frequency uncertainty of ±1/N it is impossible to determine if the peaks detected around τ=24 and τ=5 correspond to the self image of a sequence with zero time-frequency shift or another device assigned a circular shift of τ=5 or τ=24.
The ambiguity function of a Gold sequence is not as bad as a Zadoff-Chu sequence. However, there are only N+2 sequences in the set and the maximum cross correlation value √{square root over (2N)} is worse than that of the Zadoff-Chu sequence.
What is desired, therefore, and an object of the present invention, are improved method, apparatus, system, and techniques for forming and detecting a signature sequence.